The figure, not drawn to scale, O is the centre of the circle and YD // ZC // AB. Find
- ∠XOA
- ∠XCO
(a)
∠DOZ
= 180° - 102°
= 78° (Interior angles, YD//ZO)
∠OAC = ∠OCA = 29° (Isosceles triangle)
∠ZOA
= 29° + 29°
= 58° (Exterior angle of a triangle)
∠XOA
= 78° + 58°
= 136°
(b)
∠COA
= 180° - 29° -29°
= 122° (Isosceles triangle)
∠XOC
= 360° - 136° - 122°
= 102° (Angles at a point)
XO = OC = Radius
∠XCO
= (180° - 102°) ÷ 2
= 78° ÷ 2
= 39° (Isosceles triangle)
Answer(s): (a) 136°; (b) 39°